Disconnection by level sets of the discrete Gaussian free field and entropic repulsion

We derive asymptotic upper and lower bounds on the large deviation probability that the level set of the Gaussian free field on Zd, d≥3, below a level α, disconnects the discrete blow-up of a compact set A from the boundary of the discrete blow-up of a box that contains A, when the level set of the Gaussian free field above α is in a strongly percolative regime. These bounds substantially strengthen the results of [21],...
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